Session P36: Frontiers of Liquid Crystals: From Colloids to Chiral Liquid Crystals

Directed self-assembly of colloidal particles onto the chemically anchoring patterned surface in a nematic liquid crystal

The defects assisted assembly of colloidal particles works are more focused on the defects created in the bulk or the interface of nematic liquid crystal, which usually observe a group of particles spontaneously forming a chain or aggregating over the defects. The confining surface with specific 3D sculptured structures, such as pyramid or zig-zag grooves, offers the opportunity to isolate the trapped particles into certain position. Here, we explore a new method to direct self-assemble the colloidal particles through manipulating defects on the 2D geometry confined anchoring surface. Since the director of the preferred planar orientation of LCs could be manipulated by the pattern geometry and dimension, the topological defects could be engineered based on multi-stable orientation by designed 2D geometry pattern of different controllable direction at sub-micrometer dimension. We demonstrate that the designed one single middle straight stripe with disjoint two groups of straight stripe array on both side of the middle stripe as 45 angle of different orientation director could control the distortion of the disjoint gap space thus acting as defects template to trap the colloidal particles directed self-assembly at the designed positions. Through anchoring distribution on the pattern areas, geometry design of pattern, and also the external electric field applied on the system, those defects areas could be generate, erase, resume or even correct.   

Self-assembly and separation of nematic colloids through photo-patterned molecular orientation

Design and control of particles self-assembly is an important theme in colloidal science. Dispersions of colloids in a nematic liquid crystal (LC) show a diversity of self-assembled structures guided by long-range interactions. Here we describe a versatile approach to control colloidal structures through surface-patterned molecular orientation and dynamic processes of LC-enabled electrokinetics (LCEK). In presence of the electric field, the surface-imprinted pattern of molecular orientation triggers LCEK flows which transport the colloidal aggregates to specified locations. The aggregation is directed by the director gradients. Colloids that differ in surface anchoring or shape are guided into different areas of the cell, thus being sorted. The dynamic approach to control colloidal systems through LCEK in cells with patterned director field opens the opportunities in the microfluidic and lab on a chip applications.   

Directed Self-assembly of Colloidal Particles on a Blue Phase I Interface

Blue phases are liquid states of matter with a highly ordered defect structure which confers unique properties among complex fluids. In this work, a free energy model of chiral liquid crystals is used to consider the self-assembly of colloids and nanoparticles on the interface of a Blue Phase I. It is shown that the crystalline defect structure of the blue phase produces intricate, two-dimensional hexagonal and Kagome structures among the nanoparticle arrangements, with lattice parameters that depend on the type of anchoring of the liquid crystal at the particle’s surface. These parameters can be tuned via the chirality of the material, thereby offering intriguing possibilities for the creation of hierarchical materials based on the directed assembly of particles in chiral liquid crystals.   

Three-Dimensional Topological Solitons in Chiral Liquid Crystals and Ferromagnetic Colloids.

Three-dimensional knotted solitons - often called ``hopfions'' - have continuous physical fields classified by the Hopf index topological invariant and behave like particles. These hopfions arise in theories in many branches of physics, but their structure and stability are rarely accessible to direct experimental studies. We realize and characterize such static solitons in the molecular alignment fields of chiral liquid crystals and in the magnetization field of colloids with long-range ferromagnetic ordering. Our experiments agree with predictions of numerical modeling based on free energy minimization. By exploiting facile response of the soft matter host media, we demonstrate exquisite control of structure and tunable self-assembly of such solitonic ``particles''. This lecture will discuss how liquid crystals and colloids can serve as soft matter model systems in studies of structure, topology and dynamics of three-dimensional topological solitons.   

Brownian Dynamics of Colloidal Particles in Lyotropic Chromonic Liquid Crystals

We employ video microscopy to study the Brownian dynamics of colloidal particles in the nematic phase of lyotropic chromonic liquid crystals (LCLCs). These LCLCs (in this case, DSCG) are water soluble, and their nematic phases are characterized by an unusually large elastic anisotropy. Our preliminary measurements of particle mean-square displacement for polystyrene colloidal particles (\textasciitilde 5 micron-diameter) show diffusive and sub-diffusive behaviors moving parallel and perpendicular to the nematic director, respectively. In order to understand these motions, we are developing models that incorporate the relaxation of elastic distortions of the surrounding nematic field. Further experiments to confirm these preliminary results and to determine the origin of these deviations compared to simple diffusion theory are ongoing; our results will also be compared to previous diffusion experiments in nematic liquid crystals [1-3]. 1. G. J. Kr\"{u}ger, \textit{Physics Reports} \textbf{82}, 229 (1982). 2. J. C. Loudet, P. Hanusse, P. Poulin, \textit{Science} \textbf{306}, 1525 (2004) 3. T. Turiv, I. Lazo, A. Brodin, B. I. Lev, V. Reiffenrath, V. G. Nazarenko, O. D. Lavrentovich, \textit{Science}~\textbf{342}, 1351 (2013).   

Dielectric Anisotropy of Gold Nanoparticle Colloids in Nematic Liquid Crystals

We present electrical and optical studies of hexanethiol-treated gold nanoparticle (GNPs) colloids in 4-cyano-4$\prime $-pentyl-biphenyl (5CB) liquid crystals. Preliminary data analysis suggests an unusual behavior of sudden drop and then rise in the dielectric anisotropy at a critical concentration of 0.0862{\%} by wt. GNPs and a sudden rise and then drop in the nematic to isotropic transition temperature. Above the critical concentration the data level off to within the uncertainty of the experimental errors. This colloidal system will help us to understand the interaction and the effects of nanoparticles on the self-assembly of LC molecules and the manner in which these particles organize in LC. This study is important for further developments in nanotechnology, sharp and fast display panels, and within the medical field.   

Colloidal Transport within Nematics with Arrays of Obstacles

We have investigated the transport behavior of spherical colloidal particles suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) within microfluidic arrays of cylindrical obstacles arranged in a square lattice. Homeotropic anchoring at the surfaces of the obstacles created periodic director-field patterns that strongly influenced the trajectories of the colloids, which had both planar and homeotropic anchoring, as they traversed the arrays under gravity. When the applied force was along a symmetry direction of the lattice, the particles moved parallel to the force but with pronounced modulations in their velocity due to the liquid-crystal-mediated interactions with the posts. With increasing angle between the force and symmetry direction, the particle trajectories underwent a transition in which their average velocity no longer followed the force and instead was parallel to the lattice symmetry direction. The point of this transition was dictated by the particle-post interactions, suggesting a potential new mechanism for particle separations.   

Colloidal interactions and self-assembly of plasmonic metal pyramids in nematic liquid crystals.

Combining ordered structure of soft matter systems, such as liquid crystals, with the unique optical properties of metal nano- and micro-particles is a promising approach of designing and realizing mesostructured composites with pre-engineered properties. In this work, we disperse nanofabricated pyramid-shaped plasmonic particles in a nematic host fluid and demonstrate that the particles spontaneously align with respect to the uniform far-field liquid crystal director. This alignment is driven by minimization of the surface anchoring and bulk elastic free energies of the nematic host. Interestingly, multiple stable and metastable orientations of these particles can be controllably observed. Using laser tweezers and video microscopy, we explore inter-particle pair interaction forces as well as the ensuing colloidal self-assembly. We analyze this experimentally observed rich physical behavior of our soft matter composite by invoking electrostatic multipole analogy of elastic distortions induced by the particles in a nematic liquid crystal host and discuss potential practical uses.   

Co-dispersion of plasmonic nanorods in thermotropic nematic liquid crystals

Colloidal dispersions of plasmonic metal nanoparticles in liquid crystals promise the capability of pre-engineering tunable optical properties of mesostructured metal-dielectric composites. Recently, concentrated dispersions of anisotropic gold, silver, and metal alloy nanoparticles in nematic hosts have been achieved and successfully controlled by low-voltage fields [1, 2]. However, to enable versatile designs of material behavior of the composites, simultaneous co-dispersion of anisotropic particles with different shapes, alignment properties, and compositions are often needed. We achieve such co-dispersions and explore their switching characteristics in response to external stimuli like light and electric fields. We demonstrated that spectral characteristics of co-dispersions of multiple types of anisotropic nanoparticles in a common nematic host provides unprecedented variety of electrically- and optically-tunable material behavior, with a host of potential practical applications in electro-optic devices and displays. [1] Liu, Q., Yuan, Y., {\&} Smalyukh, I. I. (2014).~\textit{Nano letters},~\textit{14}(7), 4071-4077. [2] Zhang, Y., Liu, Q., Mundoor, H., Yuan, Y., {\&} Smalyukh, I. I. (2015).~\textit{ACS nano},~\textit{9}(3), 3097-3108.   

Tactoids of chiral liquid crystals

The phase diagram of chiral liquid crystals confined in ellipsoids is obtained, by following a theoretically informed Monte Carlo relaxation of the tensor alignment field $\mathbf{Q}$. The free energy of the system is described by a functional in the framework of the Landau-de~Gennes formalism. This study also includes the effect of anchoring strength, curvature, and chirality of the system. In the low chirality region of the phase diagram we found the twist bipolar (BS) phase and some cholesteric phases such as the radial spherical structure (RSS), twist cylinder (TC) and double twist cylinder (DTC) whose axis of rotation is not necessarily aligned with the major axis of the geometry. For high chirality scenarios, the disclination lines are twisted or bent near the surface preventing the formation of symmetric networks of defects, although an hexagonal pattern is formed on the surface which might serve as open sites for collocation of colloids. By analyzing the free energies of isochoric systems, prolate geometries tend to be more favorable for high chirality and low anchoring conditions.   

Chiral liquid crystals: the vestigial chiral phases of $T$, $O$, $I$ matter

We show how chiral order develops in vestigial isotropic phases of $T,O$ and $I$ liquid crystalline systems in three dimensions. The liquid crystal phases are realized in a lattice model of orientational degrees of freedom with point group symmetries $G \subset O(3)$, represented as $O(3)$-rotors coupled to $G$ gauge fields. The model incorporates also disclinations via the gauge fields, features an ordered nematic phase with unbroken $G$ rotations at low temperatures and a high temperature isotropic liquid phase. We observe an intermediate phase with spontaneous chirality but isotropic $SO(3)$ symmetry (a liquid) for the gauge groups $T$, $O$, and $I$, the proper symmetry groups of the tetrahedron, cube and icosahedron, respectively. For the other subgroups of $SO(3)$, $C_{n\leq \infty}$ and $D_{n\leq \infty}$, there is generically only a single phase transition from the nematic phase to the isotropic liquid. We discuss the nature of the phase transitions and conditions under which the chiral phase is stabilized by the nematic order parameter fluctuations. The nature of the vestigial chiral phase is reminiscent of the so-called Ising nematic phase in iron based superconductors.   

Structures of cholesteric liquid crystals confined in rectangular micro-channels

When cholesteric liquid crystals are confined in various geometries, the interplays between the boundary conditions, the bulk structures and different length scales (pitch, penetration depth, and confinement size) may cause frustration and formation of intriguing topological defects and disclination lines. This paper presents our recent studies on the structures of cholesteric liquid crystals confined in rectangular microchannels with homeotropic alignments. The rectangular microchannels with various sizes and aspect ratios are made in glass substrates by using modern nanofabrication techniques. Detailed liquid crystal structures and their optical characterizations will be presented as a function of the channel depth and width.   

Cooking skyrmions: modeling temperature dependence of defect textures in cholesteric liquid crystals

Using 3-d simulations and analytical calculations, we study temperature dependence of defect structures in~liquid crystals in confined geometries. We model a cholesteric liquid crystal confined~in a microchannel with homeotropic anchoring, and investigate resulting~defect structures---skyrmions, alone or in periodic arrays (bubble domains), and striped textures~---as a function of microchannel dimensions, cholesteric pitch, and surface anchoring strength. We model temperature dependence by varying Frank constants and pitch using functions fit to experimental values. Experiments by the Qihuo Wei group show that skyrmion arrays in a microchannel appear to ``pop'' at a threshold temperature, transforming into elongated defects that span the microchannel's width. We explore this behavior using simulation and show that skyrmions elongate when their spacing is below a critical distance. Implementation of the simulation code in CUDA for a GPU-equipped computer~produces highly efficient~performance.~~We also carry out analytical calculations of free energy to determine optimal/stable structures for skyrmions~and other defect textures in thin cells. Both simulation and analytical results are compared to recent experiments by the Qihuo Wei group.